arXiv subjects

Priyanka Roy

Publications and source records attributed to Priyanka Roy.

6 recordsLinked to original sources

arXiv2025

Online Regularized Learning Algorithms in RKHS with $\beta$- and $\phi$-Mixing Sequences

In this paper, we study an online regularized learning algorithm in a reproducing kernel Hilbert spaces (RKHS) based on a class of dependent processes. We choose such a process where the degree of dependence is measured by mixing coefficients. As a representative example, we analyze a strictly stationary Markov chain, where the dependence structure is characterized by the $\phi$- and $\beta$-mixing coefficients. Under these assumptions, we derive probabilistic upper bounds as well as convergence rates for both the exponential and polynomial decay of the mixing coefficients.

stat.ML↗

arXiv2025

Gradient Descent Algorithm in Hilbert Spaces under Stationary Markov Chains with $\phi$- and $\beta$-Mixing

In this paper, we study a strictly stationary Markov chain gradient descent algorithm operating in general Hilbert spaces. Our analysis focuses on the mixing coefficients of the underlying process, specifically the $\phi$- and $\beta$-mixing coefficients. Under these assumptions, we derive probabilistic upper bounds on the convergence behavior of the algorithm based on the exponential as well as the polynomial decay of the mixing coefficients.

stat.ML↗

arXiv2024

Markov Chain Gradient Descent in Hilbert Spaces

In this paper, we study a Markov chain-based stochastic gradient algorithm in general Hilbert spaces, aiming at approximating the optimal solution of a quadratic loss function. We establish probabilistic upper bounds on its convergence. We further extend these results to an online regularized learning algorithm in reproducing kernel Hilbert spaces, where the samples are drawn along a Markov chain trajectory.

stat.ML↗

arXiv2019

On Critical Point for Functions with Bounded Parameters

Selection of descent direction at a point plays an important role in numerical optimization for minimizing a real valued function. In this article, a descent sequence is generated for the functions with bounded parameters to obtain a critical point. First, sufficient condition for the existence of descent direction is studied for this function and then a set of descent directions at a point is determined using linear expansion. Using these results a descent sequence of intervals is generated and critical point is characterized. This theoretical development is justified with numerical example.

math.OC↗

arXiv2019

OCTID: Optical Coherence Tomography Image Database

Optical coherence tomography (OCT) is a non-invasive imaging modality which is widely used in clinical ophthalmology. OCT images are capable of visualizing deep retinal layers which is crucial for early diagnosis of retinal diseases. In this paper, we describe a comprehensive open-access database containing more than 500 highresolution images categorized into different pathological conditions. The image classes include Normal (NO), Macular Hole (MH), Age-related Macular Degeneration (AMD), Central Serous Retinopathy (CSR), and Diabetic Retinopathy (DR). The images were obtained from a raster scan protocol with a 2mm scan length and 512x1024 pixel resolution. We have also included 25 normal OCT images with their corresponding ground truth delineations which can be used for an accurate evaluation of OCT image segmentation. In addition, we have provided a user-friendly GUI which can be used by clinicians for manual (and semi-automated) segmentation.

cs.CV↗

arXiv2019

Expansion of Generalized Hukuhara Differentiable Interval Valued Function

In this article, the concept of $μ-$ monotonic property of interval-valued function in higher dimension is introduced. Expansion of interval-valued function in higher dimension is developed using this property. Generalized Hukuhara differentiability is used to derive the theoretical results. Several examples are provided to justify the theoretical developments.

math.OC↗